Only an Avocado pit

It has been sitting in my window for about 2 months...and guess what?  I have not let it run out of water, yet.  It started out as just the pit...with a little funny thing on one end when I was cutting the avocado.  At the time I thought it had potential.  Which end goes into the water?  To the internet I go.  So to make a long story short, the pit finally started to split and now it has a little root coming out... so I guess the information was correct.  I am not sure where the stem will come from...I think it will keep splitting until the stem can come out the top.  Then what do I do with it?

I will need to go back to the internet for more information.  I understand  an avocado tree grows very slow...but that is beside the point.  I can not put it outside-to cold- so I will try to find a good spot for it's pot.   We can dream of a tree ripened avocado.